314 POPULAR SCIENCE MONTHLY. 



view of afterward drawing such conclusions as we can in regard to their 

 distance. 



APPARENT DISTRIBUTION OF THE STARS IN THE SKY. 



Distribution of the Lucid Stars: Our question now is how are the 

 stars, as we see them, distributed over the sky? We know in a general 

 way that there are vastly more stars round the belt of the Milky Way 

 than in the remainder of the heavens. But we wish to know in detail 

 what the law of increase is from the poles of the galaxy to the belt itself. 



In considering any question of the number of stars in a particular 

 region of the heavens, we are met by a fundamental difficulty. We can 

 set no limit to the minuteness of stars, and the number will depend upon 

 the magnitude of those which we include in our account. As already 

 remarked, there are, at least up to a certain limit, three or four times 

 as many stars of each magnitude as of the magnitude next brighter. 

 Now, the smallest stars that can be seen, or that may be included in 

 any count, vary greatly with the power of the instrument used in 

 making the count. If we had any one catalogue, extending over the 

 whole celestial sphere, and made on an absolutely uniform plan, so that 

 we knew it included all the stars down to some given magnitude, and 

 no others, it would answer our immediate purpose. If, however, one 

 catalogue should extend only to the ninth magnitude, while another 

 should extend to the tenth, we should be led quite astray in assuming 

 that the number of stars in the two catalogues expressed the star 

 density in the regions which they covered. The one would show three 

 or four times as many stars as the other, even though the actual 

 density in the two cases were the same. 



If we could be certain, in any one case, just what the limit of 

 magnitude was for any catalogue, or if the magnitudes in different 

 catalogues always corresponded to absolutely the same brightness of 

 the star, this difficulty would be obviated. But this is the case only 

 with that limited number of stars whose brightness has been photo- 

 metrically measured. In all other cases our count must be more or 

 less uncertain. One illustration of this will suffice: 



I have already remarked that in making the photographic census 

 of the southern heavens, Gill and Kapteyn did not assume that stars of 

 which the images were equally intense on different plates were actually 

 of the same magnitude. Each plate was assumed to have a scale of its 

 own, which was fixed by comparing the intensity of the photographic 

 impressions of those stars whose magnitudes had been previously de- 

 termined with these determinations, and thus forming as it were a 

 separate scale for each plate. But, in forming the catalogue from the 

 international photographic chart of the heavens, it is assumed that the 

 photographs taken with telescopes of the same aperture, in which 



